COMMON FACTOR

TO FACTOR A NUMBER or an expression, means to write it as multiplication, that is, as a product of factors.

Example 1. Factor 30.

Solution. 30 = 2· 15 = 2· 3· 5

If we begin 30 = 5· 6, we still obtain -- apart from the order -- 5· 2· 3.

Problem 1. Factor 50.

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50 = 2· 25 = 2· 5· 5

Factoring, then, is the reverse of multiplying. When we multiply, we write

2(a + b) = 2a + 2b.

But if we switch sides and write

2a + 2b = 2(a + b),

then we have factored 2a + 2b. We can write it as the product 2(a + b).

In this sum 2a + 2b, 2 is a common factor of each term. It is a factor of 2a, and it is a factor of 2b. This Lesson is concerned exclusively with recognizing common factors; and thus with writing a sum of terms as a product. The student will see the usefulness of that as we continue.

Problem 2. Factor 3x − 3y.

3x − 3y = 3(x − y)

Problem 3. Rewrite each of the following as the product of 2x and another factor.